Remarks on q-Bernoulli numbers associated with Daehee numbers

By Hacer Ozden, I. N. Cangul, Yilmaz Simsek. 2009

160 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/396e866b6479df952642565fd994559ce80d327f

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Citations in the corpus

• Daehee Numbers and polynomials (2013, unknown): “6) ( t et − 1 )α e = ∞ ∑ n=0 B n (x) t n! , (see [1, 2, 8]) .”
• On the weighted q-Bernoulli numbers and polynomials (2010, methodology): “Cp. If q ∈ C, one normally assume |q| < 1. If q ∈ Cp, then we assume |q−1|p < p− 1 p−1, so that qx = exp(xlogq) for |x|p ≤ 1. In this paper we use the following notation: [x]q = 1−qx 1−q , (see [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]). Let UD(Zp) be the space of uniformly differ”
• New approach to q-Euler polynomials of higher order (2010, unknown): “n=0 En(x) t n! , (see [2, 3, 19-23]), where En(x) are the n-th Euler polynomials.”
• Some Identities for the Bernoulli, the Euler and the Genocchi Numbers and Polynomials (2009, unknown): “ 2 = dn−1 dX−1 l=0 (−1)l−1B n( l + x d ), for n ∈Z+. Recently, several authors have studied the generalized Euler numbers and polynomials attached to the Dirichlet’s character with odd conductor (see [1, 2, 4, 5, 7, 8, 9, 10, 11, 12]). Now, we consider the generalized Euler polynomials attached to t”
• New results on higher-order Daehee and Bernoulli numbers and polynomials (2015, methodology): “hee polynomials, Higher order Bernoulli polynomials, Matrix representation. 2010 MSC: 05A19, 11C20 , 11B73, 11T06 1 Introduction For α ∈ N, the Bernoulli polynomials of order α are defined by, see [1]-[15] t et −1 α ext = X∞ n=0 B(α) n (x) tn n! . (1.1) When x =0,B(α) n =B (α) n (0)are the Bernoulli”